PRL 105, 197401 (2010)
PHYSICAL REVIEW LETTERS
week ending
5 NOVEMBER 2010
Ultrafast Magnon Generation in an Fe Film on Cu(100)
A. B. Schmidt,1,2,* M. Pickel,1,2 M. Donath,2 P. Buczek,3 A. Ernst,3 V. P. Zhukov,4
P. M. Echenique,5 L. M. Sandratskii,3 E. V. Chulkov,5 and M. Weinelt1
1
Max-Born-Institut, Max-Born-Straße 2A, 12489 Berlin, Germany and Freie Universität Berlin,
Fachbereich Physik, Arnimallee 14, 14195 Berlin, Germany
2
Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany
3
Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle, Germany
4
Institute of the Solid State Chemistry, Russian Academy of Sciences, Pervomayskaya 91, 620219, Yekaterinburg, Russia
5
Donostia International Physics Center (DIPC), Departamento de Fı́sica de Materiales, UPV/EHU, and
Centro de Fı́sica de Materiales CFM - MPC, Centro Mixto CSIC-UPV/EHU, San Sebastián, 20018 San Sebastian, Spain
(Received 4 December 2009; revised manuscript received 19 August 2010; published 5 November 2010)
We report on a combined experimental and theoretical study of the spin-dependent relaxation processes
in the electron system of an iron film on Cu(100). Spin-, time-, energy- and angle-resolved two-photon
photoemission shows a strong characteristic dependence of the lifetime of photoexcited electrons on their
spin and energy. Ab initio calculations as well as a many-body treatment corroborate that the observed
properties are determined by relaxation processes involving magnon emission. Thereby we demonstrate
that magnon emission by hot electrons occurs on the femtosecond time scale and thus provides a
significant source of ultrafast spin-flip processes. Furthermore, engineering of the magnon spectrum
paves the way for tuning the dynamic properties of magnetic materials.
DOI: 10.1103/PhysRevLett.105.197401
PACS numbers: 78.47.J, 73.20.At, 75.30.Ds, 79.60.i
Magnons are the fundamental collective excitations of
the electron system of magnetic materials. In collinear
ferromagnets each magnon lowers the magnetization by
2B . Understanding the generation of such spin waves
away from thermal equilibrium is necessary to develop a
microscopic picture of electron relaxation processes [1,2].
The signature of magnon generation by hot electrons has
been found in spin-polarized electron energy loss spectroscopy [3], high-resolution photoemission spectra [4], and
inelastic tunneling spectroscopy [5]. However, these experiments do not address the fundamental problem of the
time required to generate a magnon. This is, in particular,
important since magnon emission by excited electrons is
commonly viewed as a slow process, occurring within
picoseconds [6]. In contrast, laser-induced magnetic phase
transitions are reported to take place in the femtosecond
range [7–9]. Though parameterized models now describe
major properties of laser-induced demagnetization dynamics, a microscopic understanding of these processes is
still under debate [10–12].
In this Letter we present a combined experimental and
theoretical approach to study ultrafast electronic dynamics
in magnetic systems. The system we consider is a 3 monolayer iron film on Cu(001), since theory predicts spin-wave
effects to be strong in Fe [13,14]. A precise two-photon
photoemission (2PPE) experiment with spin, time, energy,
and angular resolution allows us to detect characteristic
properties in the spin, energy, and momentum dependence
of the lifetime of excited states. Based on ab initio calculations of the ground state and the magnetic excitation of
the system as well as the evaluation of the electron
0031-9007=10=105(19)=197401(4)
lifetimes within a many-body treatment of the electron
self-energy, we show that the observed properties are determined by electron-magnon interaction. Our most fundamental result is that the emission of magnons by hot
electrons takes place on a femtosecond time scale. This
implies that magnon emission must be considered an important contribution to femtomagnetic properties of 3d
ferromagnets.
In our 2PPE experiment we probe the spin-dependent
decay mechanisms of photoexcited electrons occupying
image-potential states [15]. This class of surface states is
localized several angstroms in front of the surface and they
are established as the model system of choice for the study
of electron dynamics [16]. As sketched in Fig. 1(a), a first
femtosecond laser pulse @!a excites an electron from bulk
states below the Fermi level EF into the unoccupied imagepotential-state band and from there a second pulse @!b
raises the excited electron above the vacuum level Evac .
The photoelectrons are then selected by energy and their
spin polarization is determined (for further details see
Ref. [17]). Measuring the energy as a function of the
momentum parallel to the surface Eðkk Þ yields the first
and second band (n ¼ 1, 2) with a two-dimensional parabolic dispersion [18] as depicted in Fig. 1(a). Their exchange splitting is a signature of the ferromagnetic order in
the iron film at the measurement temperature of 90 K
(T=TC ¼ 0:24) [19,20].
The lifetime of electrons photoexcited to the n ¼ 1
band is accessed by shifting the time delay between pump
and probe pulse. Figure 1(b) features six of such traces
recorded at fixed kinetic energy, parallel momentum, and
197401-1
Ó 2010 The American Physical Society
(a)
0.20
0.10
0.00
0.10
0.20
4.7
3
3
4.3
-0.4
2
2
4.1
hωa
3.9
1
n=
-0.6
1
1
3
-0.2
(b) E0
2
2
E0
E – Evac (eV)
E – EF (eV)
E
2
n=
hωb
4.5
Evac
0.30
0.0
E – EF (eV)
Parallel momentum k|| (1/Å)
0.30
n=
1
(a)
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PHYSICAL REVIEW LETTERS
1
0
-2
EF
-4
-0.8
ρ
0
k||
↓
PRL 105, 197401 (2010)
ρ↓
-6
EF
FIG. 2 (color online). (a) Schematic of the n ¼ 1 imagepotential state in the gap of the surface-projected bulk bands
(filled areas). Inelastic decay processes of the image-potentialstate electrons via electron-hole pair creation are indicated
(processes 1, 2, 3). (b) Calculated spin-resolved density of states
for the surface layer of 3 monolayer iron on Cu(100).
majority spin bulk states minority spin bulk states
(b)
1
1
Majority
0.1
Minority
2
↓
Intensity (arb. units)
2
1
τ
3
=
τ↓ =
3
15fs
18fs
0.01
11fs
15fs
Measurement
Simulation
Cross correlation
0.001
-100
0
100
Measurement
Simulation
Cross correlation
11fs
200 -100
Pump-probe delay (fs)
0
7fs
100
200
Pump-probe delay (fs)
FIG. 1 (color online). (a) Dispersing first (n ¼ 1) and second
(n ¼ 2) image-potential-state band as a function of momentum
parallel to the surface. The intensity of the 2PPE signal in the
majority- (left-hand side) and the minority-spin channel (righthand side) is presented in a contour plot with white indicating the
maximum. The arrows depict the 2PPE process schematically.
(b) Time-resolved 2PPE measurements of the n ¼ 1 imagepotential state taken at kk -values 1, 2, and 3 indicated in the
top panel.
spin projection corresponding to points 1, 2 and 3 in
Fig. 1(a). The cross correlation of the Shockley surface state
measured on clean Cu(111) (black diamonds) independently provides pulse durations and zero time delay.
Simulations with optical Bloch equations (solid lines)
yield the lifetimes " and # indicated close to the traces in
Fig. 1(b) [21,22]. Where the shift of the time-resolved traces
with respect to the cross correlation is smallest and the slope
at positive delay is steepest, the lifetimes are shortest. Hence
the time-resolved measurements demonstrate that
minority-spin electrons decay faster than majority-spin
electrons and that both, " and # , decrease significantly
with increasing momentum kk , and thus energy.
It is well established, that the decay of the excited
image-potential electrons is dominated by inelastic
electron-electron scattering, while electron-phonon scattering is negligible [16,23]. The three possible electronic
decay channels are sketched in Fig. 2(a). Process 1 describes decay into empty bulk states. In this inelastic scattering process momentum and energy are conserved by an
electron-hole pair excited in the iron film [upward-pointing
arrow in Fig. 2(a)]. A first-principles calculation of the
density of states for the surface layer is shown in Fig. 2(b).
The d bands in the majority-spin channel are almost fully
occupied, while the d states in the minority-spin channel
form a partially occupied band, exchange split from the
majority bands by about 2.5 eV. It is this spin-dependent
density of d states, which determines the difference
in majority and minority decay rates " ¼ 1=" and
# ¼ 1=# at the band minimum E0 [24,25], i.e., at
E E0 ¼ 0 eV in Fig. 3.
With increasing energy E above E0 , both decay rates
increase linearly. However, as can be seen in Fig. 3, the
minority-spin slope is twice as large as the slope for
majority-spin electrons [d# =dE ¼ 0:25 0:04 ðeV fsÞ1
vs d" =dE ¼ 0:12 0:02 ðeV fsÞ 1 ]. This large difference
in the energy dependence of the decay rates for electron
states with opposite spin projections is the most important
experimental finding of this work.
On the nonmagnetic Cu(100) surface the increase of
decay rate with increasing energy above E0 is due to interband scattering and intraband scattering [processes 2 and 3
in Fig. 2(a)]: The electrons gain additional phase space for
decay (hatched area in Fig. 2) [23,26]. Likewise in iron, this
additional phase space is comprised of the two-dimensional
image-potential band (constant density of states) and the sp
bulk bands at energies E > E0 [cf. Figure 2(b)]. While this
will lead to an increase of the decay rate, the additional
phase space is hardly spin dependent and therefore cannot
account for the large difference observed in the slope
d=dE between minority and majority electrons.
This difference originates from the spin asymmetry of
magnon emission driven by hot electron decay. In a spinflip scattering event the excited electron occupies initial
and final states corresponding to opposite spin projections.
Since the spin-flip transition is associated with a change of
the spin angular momentum of the hot electron, a direct
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PRL 105, 197401 (2010)
PHYSICAL REVIEW LETTERS
0.25
Γ↓
0.10
Γ
0.05
0.0
0.1
0.2
0.3
0.4
0.5
Energy above band minimum E – E0 (eV)
FIG. 3 (color online). Decay rate ¼ 1= of the first imagepotential states on the iron film in the majority- and minorityspin band for increasing energy above the band minimum. The
measured decay rates "# (symbols) are compared with the decay
rates of bulk electrons calculated in the GW (dashed lines) and
GW þ T-matrix (solid lines) formalisms.
transition is allowed only under the influence of spin-orbit
coupling. In our case spin-orbit coupling is very weak and
direct spin-flip processes have negligible contribution to
the decay rate. There is, however, another scenario leading
to the change of the spin projection of the hot electron. This
is an exchange process where the hot electron interacts
with the electrons of the film. Such a process is depicted in
Fig. 4(a). At the end, the excited electron has opposite spin
projection with a smaller energy and, simultaneously, there
is a compensating spin-flip process in the film. The latter
can be either a single electron spin reversal (Stoner excitation) or a collective electron excitation (spin wave). In
general, both, Stoner excitation and magnon can be emitted
and absorbed in the exchange-scattering process within the
constraints of energy and momentum conservation.
Because of the low temperature of our experiment, we
can neglect absorption. Since the Stoner excitations have
(b)
n=1
(a)
E
0.2
e↓
e
∆k||
∆E
e↓
k||
minority
0
q1
0.0
-0.2
h
majority
–1
k|| = 0.1 Å
q2
q3
q0
-0.1
↓
EF
–1
k|| = 0 Å
0.1
qy (1/Å)
↓
(c)
k||
-0.1
0.0
0.1
Energy hω (eV)
0.15
↓
Decay rate Γ (1/fs)
characteristic energies of the order of the exchange splitting of 2.5 eV, they will not play a role in the decay
processes 2 and 3 with energy transfers below 0.5 eV. In
this energy range magnons can play a dominant role in the
lifetime of minority electrons [14], since the magnon spectrum starts at zero energy. We demonstrate in the following
that magnon emission is responsible for our observations.
In Fig. 4(c) we show the calculated spin-flip spectrum of
the film. There are three spin-wave branches: one acoustic
starting with zero energy and two optical with activation
energies around 0.1 eV. The characteristic form of the
spectrum with the parabolic dispersion of optical magnons
is a consequence of the exchange interactions in the film
that are stronger within than between the atomic planes.
The calculations are based on a new implementation of the
linear response density functional theory (LRDFT)
[27,28]. LRDFT allows us to determine the transverse
magnetic susceptibility ðqk ; !Þ of the film, taking into
account our calculated band structure and thus the influence of the surface and the hybridization of the electronic
states in the iron layers with the nonmagnetic substrate.
Because of the nearly half-metallic character of the film the
number of Stoner states in the spin-wave energy region is
small and the magnon peaks are well defined [28].
As energy @! and momentum qk are transferred to the
magnon, the conservation laws imply @!ðqk Þ ¼ E# ðkk Þ E" ðkk qk Þ. Considering the dispersion relations of electrons and spin waves, for a minority electron residing at the
band minimum ( point) the phase space available for
decay with magnon emission is severely limited. Since
the spin splitting of the image-potential-state band is
smaller than the activation energy of the optical spin
waves, only decay into acoustic magnons is possible.
Moreover, energy and momentum conservation restricts
the number of available acoustic magnons to those with
1 [cf. Fig. 4(b)]. As the momentum of the
q0 0:09 A
primary electron kk rises, there are more accessible acous 1
tic magnon states [illustrated in Fig. 4(b) for kk 0:1 A
by the ring q1 ]. Additionally, new decay channels open,
Exp. majority
Exp. minority
GW majority
GW+T majority
GW minority
GW+T minority
0.20
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0.2
qx (1/Å)
FIG. 4 (color). (a) Schematic illustration of an exchange spin-flip process. (b) Spin-wave states accessible by decaying image 1 (dashed line) and kk ¼ 0:1 A
1 (solid lines) along X . Rings q0
potential-state minority electrons for initial momenta kk ¼ 0 A
and q1 denote final magnon states in the acoustic mode, q2 and q3 in the low and high energy optical branches, respectively.
(c) Spectral power =ðqk ; @!Þ of spin-flip excitations in 3 monolayer iron on Cu(100) obtained from LRDFT calculations.
197401-3
PRL 105, 197401 (2010)
PHYSICAL REVIEW LETTERS
corresponding to the generation of optical spin waves at the
smaller momenta q2 and q3 . This increase in phase space
explains why, with the onset of magnon emission, the
decay rate of the minority electrons increases more steeply
with their initial energy.
In the framework of many-body theory, the decay rate of
an excited electron can be derived from the imaginary part
of the electron self-energy as ¼ 2@1 Im. Different
approximations for account for different excitations in
the system that compensate the electron’s transition. We
performed calculations within two schemes: In the socalled GW approximation to collective excitations of
the spin-wave type are not taken into account. Only singleparticle spin-flip excitations (Stoner excitations) are incorporated. In the scheme we refer to as GW þ T (GW plus T
matrix), multiple scattering of the Stoner’s electron-hole
pairs is included. In this formalism the latter gives rise to
spin-wave excitations. The decay rates of bulk electrons
calculated via the GW and GW þ T approaches at excitation energies corresponding to the energy losses in intraband and interband decay (processes 2 and 3) are shown as
dashed and solid lines in Fig. 3, respectively. The decay
rates have been scaled by the bulk penetration of the
image-potential states at the band bottom and are multiplied by 2=3 to account for the two-dimensionality of the
thin iron film. The comparison between GW and GW þ T
confirms that magnon emission at low excitation energies
yields a dominating contribution to the decay rate # [13]
and provides a much higher slope d# =dE for spinminority electrons. Our considerations show that the physical mechanism leading to the different energy dependence
of " and # is the emission of spin waves by the minority
electrons.
The emission of magnons must take place on the femtosecond time scale, since the lifetime of these hot electrons
is in the femtosecond range and the contribution of magnon
emission to the decay rate of spin-down electrons is large.
This establishes the time scale it requires to create a
magnon in an itinerant ferromagnet. It is independent of
the electronic state used to probe magnon emission,
whether surface or bulk state. Our theoretical studies for
bulk iron corroborate the magnon emission time at the
scale of the lifetime of hot electrons.
The efficiency of magnon generation by hot electrons,
on the other hand, depends on the accessibility of the spinwave states ruled by energy and momentum conservation
and is therefore material dependent. This dependence has
been observed for the 3d ferromagnets [13,29]. Extending
our combined approach to Co films, first results show an
increase of with a weaker spin dependence. In contrast to
the Fe films, here the exchange coupling is of comparable
magnitude in and between the layers. Therefore the optical
magnons in the Co films have much higher energies and
cannot contribute to the decay of electrons at low excitation energies.
In conclusion, we found that the increase of the decay
rate of image-potential-state electrons with increasing
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energy is highly spin dependent in iron films. This result
can be explained by many-body theory of the excited
electron lifetime only if magnon generation is taken into
account. We have established that the generation of collective magnetic excitations takes place on a femtosecond
time scale. Hot electrons are assumed to drive ultrafast
magnetization dynamics through spin-flip electron scattering [11]. Here we show that magnon emission provides a
significant microscopic source for ultrafast spin-flip processes. We could capture microscopic details of electronmagnon coupling uncovering which electrons and
magnons are involved. Our results indicate that tuning
the spin-selective decay rate of injected electrons could
be achieved through engineering of the acoustical and
optical branches of the spin-wave dispersion via the material and structural properties of the thin film.
Financial support by the Deutsche Forschungsgemeinschaft, UPV/EHU (Grant No. IT-366-07), and
MCyT (Grant No. FIS2007-66711-C02-01) is gratefully
acknowledged.
*[email protected]
R. Huber et al., Nature (London) 414, 286 (2001).
M. Hase et al., Nature (London) 426, 51 (2003).
R. Vollmer et al., Phys. Rev. Lett. 91, 147201 (2003).
J. Schäfer et al., Phys. Rev. Lett. 92, 097205 (2004).
T. Balashov et al., Phys. Rev. Lett. 97, 187201 (2006).
J. Stöhr and H.-C. Siegmann, Magnetism. From Fundamentals to Nanoscale Dynamics (Springer, Berlin, 2006).
[7] E. Beaurepaire et al., Phys. Rev. Lett. 76, 4250 (1996).
[8] C. D. Stanciu et al., Phys. Rev. Lett. 99, 047601 (2007).
[9] J.-Y. Bigot, M. Vomir, and E. Beaurepaire, Nature Phys. 5,
515 (2009).
[10] B. Koopmans et al., Phys. Rev. Lett. 85, 844 (2000).
[11] B. Koopmans et al., Nature Mater. 9, 259 (2010).
[12] M. Battiato, K. Carva, and P. M. Oppeneer, Phys. Rev.
Lett. 105, 027203 (2010).
[13] V. P. Zhukov, E. V. Chulkov, and P. M. Echenique, Phys.
Rev. Lett. 93, 096401 (2004).
[14] J. Hong and D. L. Mills, Phys. Rev. B 62, 5589 (2000).
[15] P. M. Echenique and J. B. Pendry, J. Phys. C 11, 2065
(1978).
[16] P. M. Echenique et al., Surf. Sci. Rep. 52, 219 (2004).
[17] M. Weinelt et al., Prog. Surf. Sci. 82, 388 (2007).
[18] J. Güdde et al., Science 318, 1287 (2007).
[19] J. Thomassen et al., Phys. Rev. Lett. 69, 3831 (1992).
[20] A. B. Schmidt et al., Phys. Rev. Lett. 95, 107402 (2005).
[21] K. Blum, Density Matrix Theory and Applications
(Plenum, New York, 1981).
[22] T. Hertel et al., Phys. Rev. Lett. 76, 535 (1996).
[23] M. Weinelt, J. Phys. Condens. Matter 14, R1099 (2002).
[24] F. Passek et al., Phys. Rev. Lett. 75, 2746 (1995).
[25] M. Aeschlimann et al., Phys. Rev. Lett. 79, 5158 (1997).
[26] W. Berthold et al., Phys. Rev. Lett. 88, 056805 (2002).
[27] E. K. U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850
(1985).
[28] P. Buczek et al., Phys. Rev. Lett. 102, 247206 (2009).
[29] W. X. Tang et al., Phys. Rev. Lett. 99, 087202 (2007).
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